If pp is false and qq is false, find the truth value of:
p, and, \neg, q
p∧¬q

Given that \( p \) is false and \( q \) is false, let's evaluate the expression \( p \land \neg q \).

### Step 1: Identify the truth values
- \( p = \text{false} \)
- \( q = \text{false} \)

### Step 2: Determine the truth value of \( \neg q \)
- \( \neg q \) is the negation of \( q \).
- Since \( q = \text{false} \), \( \neg q = \text{true} \).

### Step 3: Evaluate \( p \land \neg q \)
- \( p \land \neg q \) is the logical "and" of \( p \) and \( \neg q \).
- The "and" (\( \land \)) operation is true only if both operands are true.

In this case:
- \( p = \text{false} \)
- \( \neg q = \text{true} \)

Since one of the operands is false, \( p \land \neg q \) is **false**.

### Final Answer:
The truth value of \( p \land \neg q \) is **false**.

Would you like more details or have any questions about this? 

Here are some related questions to explore:
1. What is the truth table for the conjunction (\( \land \)) operation?
2. How does the truth value change if \( p \) is true and \( q \) is false?
3. What is the truth value of \( \neg (p \land q) \) given \( p = \text{false} \) and \( q = \text{false} \)?
4. How do logical operators like \( \land \) and \( \neg \) relate to circuits in computer science?
5. What happens if both \( p \) and \( q \) are true in the expression \( p \land \neg q \)?

**Tip:** When working with logical expressions, constructing a truth table can be a helpful way to visualize all possible outcomes.

Explore how to evaluate the logical expression p ∧ ¬q when given that p is false and q is false. Understand the concept of logical conjunction and negation in boolean algebra. Suitable for high school students and those interested in logic and boolean algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation